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Reinforcement Learning · Function Approximation

Kishan Panaganti, Adam Wierman, Eric Mazumdar

The robust $\phi$-regularized Markov Decision Process (RRMDP) framework focuses on designing control policies that are robust against parameter uncertainties due to mismatches between the simulator (nominal) model and real-world settings. This work makes *two* important contributions. First, we propose a *model-free* algorithm called *Robust $\phi$-regularized fitted Q-iteration* for learning an $\epsilon$-optimal robust policy that uses only the historical data collected by rolling out a behavior policy (with *robust exploratory* requirement) on the nominal model. To the best of our knowledge, we provide the *first* unified analysis for a class of $\phi$-divergences achieving robust optimal policies in high-dimensional systems of arbitrary large state space with general function approximation. Second, we introduce the *hybrid robust $\phi$-regularized reinforcement learning* framework to learn an optimal robust policy using both historical data and online sampling. Towards this framework, we propose a model-free algorithm called *Hybrid robust Total-variation-regularized Q-iteration*. To the best of our knowledge, we provide the *first* improved out-of-data-distribution assumption in large-scale problems of arbitrary large state space with general function approximation under the hybrid robust $\phi$-regularized reinforcement learning framework.

Optimization · Learning for Optimization

Jiarong Pan, Stefan Falkner, Felix Berkenkamp, Joaquin Vanschoren

Bayesian optimization (BO) is a popular method to optimize costly black-box functions, and meta-learning has emerged as a way to leverage knowledge from related tasks to optimize new tasks faster. However, existing meta-learning methods for BO rely on surrogate models that are not scalable or are sensitive to varying input scales and noise types across tasks. Moreover, they often overlook the uncertainty associated with task similarity, leading to unreliable task adaptation when a new task differs significantly or has not been sufficiently explored yet. We propose a novel meta-learning BO approach that bypasses the surrogate model and directly learns the utility of queries across tasks. It explicitly models task uncertainty and includes an auxiliary model to enable robust adaptation to new tasks. Extensive experiments show that our method achieves strong performance and outperforms multiple meta-learning BO methods across various benchmarks.

Deep Learning · Graph Neural Networks

Dominik Fuchsgruber, Tom Wollschläger, Bertrand Charpentier, Antonio Oroz, Stephan Günnemann

Uncertainty Sampling is an Active Learning strategy that aims to improve the data efficiency of machine learning models by iteratively acquiring labels of data points with the highest uncertainty. While it has proven effective for independent data its applicability to graphs remains under-explored. We propose the first extensive study of Uncertainty Sampling for node classification: **(1)** We benchmark Uncertainty Sampling beyond predictive uncertainty and highlight a significant performance gap to other Active Learning strategies. **(2)** We develop ground-truth Bayesian uncertainty estimates in terms of the data generating process and prove their effectiveness in guiding Uncertainty Sampling toward optimal queries. We confirm our results on synthetic data and design an approximate approach that consistently outperforms other uncertainty estimators on real datasets. **(3)** Based on this analysis, we relate pitfalls in modeling uncertainty to existing methods. Our analysis enables and informs the development of principled uncertainty estimation on graphs.

Reinforcement Learning

Mattie Fellows, Brandon Kaplowitz, Christian Schroeder de Witt, Shimon Whiteson

Bayesian reinforcement learning (RL) offers a principled and elegant approach for sequential decision making under uncertainty. Most notably, Bayesian agents do not face an exploration/exploitation dilemma, a major pathology of frequentist methods. However theoretical understanding of model-free approaches is lacking. In this paper, we introduce a novel Bayesian model-free formulation and the first analysis showing that model-free approaches can yield Bayes-optimal policies. We show all existing model-free approaches make approximations that yield policies that can be arbitrarily Bayes-suboptimal. As a first step towards model-free Bayes optimality, we introduce the Bayesian exploration network (BEN) which uses normalising flows to model both the aleatoric uncertainty (via density estimation) and epistemic uncertainty (via variational inference) in the Bellman operator. In the limit of complete optimisation, BEN learns true Bayes-optimal policies, but like in variational expectation-maximisation, partial optimisation renders our approach tractable. Empirical results demonstrate that BEN can learn true Bayes-optimal policies in tasks where existing model-free approaches fail.

Reinforcement Learning

Navdeep Kumar, Kaixin Wang, Kfir Levy, Shie Mannor

We focus on s-rectangular robust Markov decision processes (MDPs), which capture interconnected uncertainties across different actions within each state. This framework is more general compared to sa-rectangular robust MDPs, where uncertainties in each action are independent. However, the introduced interdependence significantly amplifies the complexity of the problem. Existing methods either have slow performance guarantees or are inapplicable to even moderately large state spaces. In this work, we derive optimal robust Bellman operators in explicit forms. This leads to robust value iteration methods with significantly faster time complexities than existing approaches, which can be used in large state spaces. Further, our findings reveal that the optimal policies demonstrate a novel threshold behavior, selectively favoring a limited set of actions based on their respective advantage functions. Additionally, our study uncovers a noteworthy connection between the robustness of a policy and the variance in its value function, highlighting that policies with lower variance exhibit greater resilience.

Reinforcement Learning · Batch/Offline

Dake Zhang, Boxiang Lyu, Shuang Qiu, Mladen Kolar, Tong Zhang

We study risk-sensitive reinforcement learning (RL), a crucial field due to its ability to enhance decision-making in scenarios where it is essential to manage uncertainty and minimize potential adverse outcomes. Particularly, our work focuses on applying the entropic risk measure to RL problems. While existing literature primarily investigates the online setting, there remains a large gap in understanding how to efficiently derive a near-optimal policy based on this risk measure using only a pre-collected dataset. We center on the linear Markov Decision Process (MDP) setting, a well-regarded theoretical framework that has yet to be examined from a risk-sensitive standpoint. In response, we introduce two provably sample-efficient algorithms. We begin by presenting a risk-sensitive pessimistic value iteration algorithm, offering a tight analysis by leveraging the structure of the risk-sensitive performance measure. To further improve the obtained bounds, we propose another pessimistic algorithm that utilizes variance information and reference-advantage decomposition, effectively improving both the dependence on the space dimension $d$ and the risk-sensitivity factor. To the best of our knowledge, we obtain the first provably efficient risk-sensitive offline RL algorithms.

Theory · Optimization

Bo Sun, Jerry Huang, Nicolas Christianson, Mohammad Hajiesmaili, Adam Wierman, Raouf Boutaba

The burgeoning field of algorithms with predictions studies the problem of using possibly imperfect machine learning predictions to improve online algorithm performance. While nearly all existing algorithms in this framework make no assumptions on prediction quality, a number of methods providing uncertainty quantification (UQ) on machine learning models have been developed in recent years, which could enable additional information about prediction quality at decision time. In this work, we investigate the problem of optimally utilizing uncertainty-quantified predictions in the design of online algorithms. In particular, we study two classic online problems, ski rental and online search, where the decision-maker is provided predictions augmented with UQ describing the likelihood of the ground truth falling within a particular range of values. We demonstrate that non-trivial modifications to algorithm design are needed to fully leverage the UQ predictions. Moreover, we consider how to utilize more general forms of UQ, proposing an online learning framework that learns to exploit UQ to make decisions in multi-instance settings.

Applications · Robotics

Runze Liu, Yali Du, Fengshuo Bai, Jiafei Lyu, Xiu Li

In preference-based Reinforcement Learning (RL), obtaining a large number of preference labels are both time-consuming and costly. Furthermore, the queried human preferences cannot be utilized for the new tasks. In this paper, we propose Zero-shot Cross-task Preference Alignment and Robust Reward Learning (PEARL), which learns policies from cross-task preference transfer without any human labels of the target task. Our contributions include two novel components that facilitate the transfer and learning process. The first is Cross-task Preference Alignment (CPA), which transfers the preferences between tasks via optimal transport. The key idea of CPA is to use Gromov-Wasserstein distance to align the trajectories between tasks, and the solved optimal transport matrix serves as the correspondence between trajectories. The target task preferences are computed as the weighted sum of source task preference labels with the correspondence as weights. Moreover, to ensure robust learning from these transferred labels, we introduce Robust Reward Learning (RRL), which considers both reward mean and uncertainty by modeling rewards as Gaussian distributions. Empirical results on robotic manipulation tasks from Meta-World and Robomimic demonstrate that our method is capable of transferring preference labels across tasks accurately and then learns well-behaved policies. Notably, our approach significantly exceeds existing methods when there are few human preferences. The code and videos of our method are available at: https://sites.google.com/view/pearl-preference.

Optimization · Optimization and Learning under Uncertainty

Jonas Beck, Nathanael Bosch, Michael Deistler, Kyra Kadhim, Jakob Macke, Philipp Hennig, Philipp Berens

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would allow for gradient-based parameter optimization, the nonlinear dynamics of ODEs often lead to many local minima and extreme sensitivity to initial conditions. We therefore propose diffusion tempering, a novel regularization technique for probabilistic numerical methods which improves convergence of gradient-based parameter optimization in ODEs. By iteratively reducing a noise parameter of the probabilistic integrator, the proposed method converges more reliably to the true parameters. We demonstrate that our method is effective for dynamical systems of different complexity and show that it obtains reliable parameter estimates for a Hodgkin--Huxley model with a practically relevant number of parameters.

Reinforcement Learning

Junkai Zhang, Weitong Zhang, Dongruo Zhou, Quanquan Gu

Mastering multiple tasks through exploration and learning in an environment poses a significant challenge in reinforcement learning (RL). Unsupervised RL has been introduced to address this challenge by training policies with intrinsic rewards rather than extrinsic rewards. However, current intrinsic reward designs and unsupervised RL algorithms often overlook the heterogeneous nature of collected samples, thereby diminishing their sample efficiency. To overcome this limitation, in this paper, we proposed a reward-free RL algorithm called GFA-RFE. The key idea behind our algorithm is an uncertainty-aware intrinsic reward for exploring the environment and an uncertainty-weighted learning process to handle heterogeneous uncertainty in different samples. Theoretically, we show that in order to find an $\epsilon$-optimal policy, GFA-RFE needs to collect $\tilde{O} (H^2 \log N_{\mathcal{F}} (\epsilon) \text{dim} (\mathcal{F}) / \epsilon^2 )$ number of episodes, where $\mathcal{F}$ is the value function class with covering number $N_{\mathcal{F}} (\epsilon)$ and generalized eluder dimension $\text{dim} (\mathcal{F})$. Such a result outperforms all existing reward-free RL algorithms. We further implement and evaluate GFA-RFE across various domains and tasks in the DeepMind Control Suite. Experiment results show that GFA-RFE outperforms or is comparable to the performance of state-of-the-art unsupervised RL algorithms.

Theory · Reinforcement Learning and Planning

Kaiwen Wang, Owen Oertell, Alekh Agarwal, Nathan Kallus, Wen Sun

In this paper, we prove that Distributional Reinforcement Learning (DistRL), which learns the return distribution, can obtain second-order bounds in both online and offline RL in general settings with function approximation. Second-order bounds are instance-dependent bounds that scale with the variance of return, which we prove are tighter than the previously known small-loss bounds of distributional RL. To the best of our knowledge, our results are the first second-order bounds for low-rank MDPs and for offline RL. When specializing to contextual bandits (one-step RL problem), we show that a distributional learning based optimism algorithm achieves a second-order worst-case regret bound, and a second-order gap dependent bound, simultaneously. We also empirically demonstrate the benefit of DistRL in contextual bandits on real-world datasets. We highlight that our analysis with DistRL is relatively simple, follows the general framework of optimism in the face of uncertainty and does not require weighted regression. Our results suggest that DistRL is a promising framework for obtaining second-order bounds in general RL settings, thus further reinforcing the benefits of DistRL.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Zhiyu Zhang, David Bombara, Heng Yang

We study online learning in adversarial nonstationary environments. Since the future can be very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we revisit the discounted regret in online convex optimization, and propose an adaptive (i.e., instance optimal), FTRL-based algorithm that improves the widespread non-adaptive baseline -- gradient descent with a constant learning rate. From a practical perspective, this refines the classical idea of regularization in lifelong learning: we show that designing better regularizers can be guided by the principled theory of adaptive online optimization. Complementing this result, we also consider the (Gibbs & Candes, 2021)-style online conformal prediction problem, where the goal is to sequentially predict the uncertainty sets of a black-box machine learning model. We show that the FTRL nature of our algorithm can simplify the conventional gradient-descent-based analysis, leading to instance-dependent performance guarantees.

Optimization · Optimization and Learning under Uncertainty

Ali Zeynali, Shahin Kamali, Mohammad Hajiesmaili

We present the first learning-augmented data structure for implementing dictionaries with optimal consistency and robustness. Our data structure, named RobustSL, is a Skip list augmented by predictions of access frequencies of elements in a data sequence. With proper predictions, RobustSL has optimal consistency (achieves static optimality). At the same time, it maintains a logarithmic running time for each operation, ensuring optimal robustness, even if predictions are generated adversarially. Therefore, RobustSL has all the advantages of the recent learning-augmented data structures of Lin, Luo, and Woodruff (ICML 2022) and Cao et al. (arXiv 2023), while providing robustness guarantees that are absent in the previous work. Numerical experiments show that RobustSL outperforms alternative data structures using both synthetic and real datasets.

Reinforcement Learning · Function Approximation

Chenlu Ye, Jiafan He, Quanquan Gu, Tong Zhang

This study tackles the challenges of adversarial corruption in model-based reinforcement learning (RL), where the transition dynamics can be corrupted by an adversary. Existing studies on corruption-robust RL mostly focus on the setting of model-free RL, where robust least-square regression is often employed for value function estimation. However, these techniques cannot be directly applied to model-based RL. In this paper, we focus on model-based RL and take the maximum likelihood estimation (MLE) approach to learn transition model. Our work encompasses both online and offline settings. In the online setting, we introduce an algorithm called corruption-robust optimistic MLE (CR-OMLE), which leverages total-variation (TV)-based information ratios as uncertainty weights for MLE. We prove that CR-OMLE achieves a regret of $\tilde{\mathcal{O}}(\sqrt{T} + C)$, where $C$ denotes the cumulative corruption level after $T$ episodes. We also prove a lower bound to show that the additive dependence on $C$ is optimal. We extend our weighting technique to the offline setting, and propose an algorithm named corruption-robust pessimistic MLE (CR-PMLE). Under a uniform coverage condition, CR-PMLE exhibits suboptimality worsened by $\mathcal{O}(C/n)$, nearly matching the lower bound. To the best of our knowledge, this is the first work on corruption-robust model-based RL algorithms with provable guarantees.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

TengYe Xu, Zihao Li, Qinyuan Ren

A key challenge in Meta-Reinforcement Learning (meta-RL) is the task distribution shift, since the generalization ability of most current meta-RL methods is limited to tasks sampled from the training distribution. In this paper, we propose Posterior Sampling Bayesian Lifelong In-Context Reinforcement Learning (PSBL), which is robust to task distribution shift. PSBL meta-trains a variant of transformer to directly perform amortized inference about the Predictive Posterior Distribution (PPD) of the optimal policy. Once trained, the network can infer the PPD online with frozen parameters. The agent then samples actions from the approximate PPD to perform online exploration, which progressively reduces uncertainty and enhances performance in the interaction with the environment. This property is known as in-context learning. Experimental results demonstrate that PSBL significantly outperforms standard Meta RL methods both in tasks with sparse rewards and dense rewards when the test task distribution is strictly shifted from the training distribution.

Optimization · Optimization and Learning under Uncertainty

Ziyad Benomar, Vianney Perchet

The non-clairvoyant scheduling problem has gained new interest within learning-augmented algorithms, where the decision-maker is equipped with predictions without any quality guarantees. In practical settings, access to predictions may be reduced to specific instances, due to cost or data limitations. Our investigation focuses on scenarios where predictions for only $B$ job sizes out of $n$ are available to the algorithm. We first establish near-optimal lower bounds and algorithms in the case of perfect predictions. Subsequently, we present a learning-augmented algorithm satisfying the robustness, consistency, and smoothness criteria, and revealing a novel tradeoff between consistency and smoothness inherent in the scenario with a restricted number of predictions.

Optimization · Large Scale, Parallel and Distributed

Jiaqi Wang, Chenxu Zhao, Lingjuan Lyu, Quanzeng You, Mengdi Huai, Fenglong Ma

This paper presents FedType, a simple yet pioneering framework designed to fill research gaps in heterogeneous model aggregation within federated learning (FL). FedType introduces small identical proxy models for clients, serving as agents for information exchange, ensuring model security, and achieving efficient communication simultaneously. To transfer knowledge between large private and small proxy models on clients, we propose a novel uncertainty-based asymmetrical reciprocity learning method, eliminating the need for any public data. Comprehensive experiments conducted on benchmark datasets demonstrate the efficacy and generalization ability of FedType across diverse settings. Our approach redefines federated learning paradigms by bridging model heterogeneity, eliminating reliance on public data, prioritizing client privacy, and reducing communication costs (The codes are available in the supplementation materials).

Theory · Optimization

Yafei Wang, Bo Pan, Mei Li, Jianya Lu, Lingchen Kong, Bei Jiang, Linglong Kong

Conditional Stochastic Optimization (CSO) is a powerful modelling paradigm for optimization under uncertainty. The existing literature on CSO is mainly based on the independence assumption of data, which shows that the solution of CSO is asymptotically consistent and enjoys a finite sample guarantee. The independence assumption, however, does not typically hold in many important applications with dependence patterns, such as time series analysis, operational control, and reinforcement learning. In this paper, we aim to fill this gap and consider a Sample Average Approximation (SAA) for CSO with dependent data. Leveraging covariance inequalities and independent block sampling technique, we provide theoretical guarantees of SAA for CSO with dependent data. In particular, we show that SAA for CSO retains asymptotic consistency and a finite sample guarantee under mild conditions. In addition, we establish the sample complexity $O(d / \varepsilon^4)$ of SAA for CSO, which is shown to be of the same order as independent cases. Through experiments on several applications, we verify the theoretical results and demonstrate that dependence does not degrade the performance of the SAA approach in real data applications.

Reinforcement Learning

Tao Wang, Sylvia Herbert, Sicun Gao

Policy gradient methods have enabled deep reinforcement learning (RL) to approach challenging continuous control problems, even when the underlying systems involve highly nonlinear dynamics that generate complex non-smooth optimization landscapes. We develop a rigorous framework for understanding how policy gradient methods mollify non-smooth optimization landscapes to enable effective policy search, as well as the downside of it: while making the objective function smoother and easier to optimize, the stochastic objective deviates further from the original problem. We demonstrate the equivalence between policy gradient methods and solving backward heat equations. Following the ill-posedness of backward heat equations from PDE theory, we present a fundamental challenge to the use of policy gradient under stochasticity. Moreover, we make the connection between this limitation and the uncertainty principle in harmonic analysis to understand the effects of exploration with stochastic policies in RL. We also provide experimental results to illustrate both the positive and negative aspects of mollification effects in practice.

Reinforcement Learning · Batch/Offline

Shenghua Wan, Ziyuan Chen, Le Gan, Shuai Feng, De-Chuan Zhan

Model-based offline reinforcement Learning (RL) is a promising approach that leverages existing data effectively in many real-world applications, especially those involving high-dimensional inputs like images and videos. To alleviate the distribution shift issue in offline RL, existing model-based methods heavily rely on the uncertainty of learned dynamics. However, the model uncertainty estimation becomes significantly biased when observations contain complex distractors with non-trivial dynamics. To address this challenge, we propose a new approach - *Separated Model-based Offline Policy Optimization* (SeMOPO) - decomposing latent states into endogenous and exogenous parts via conservative sampling and estimating model uncertainty on the endogenous states only. We provide a theoretical guarantee of model uncertainty and performance bound of SeMOPO. To assess the efficacy, we construct the Low-Quality Vision Deep Data-Driven Datasets for RL (LQV-D4RL), where the data are collected by non-expert policy and the observations include moving distractors. Experimental results show that our method substantially outperforms all baseline methods, and further analytical experiments validate the critical designs in our method. The project website is https://sites.google.com/view/semopo.